The first Royal Navy light warship class designed to carry a helicopter was the 'County' class of destroyers, which entered service at the start of the 1960s. These ships began to be designed primarily as large surface combatants, as a replacement for a failed design known as "the Cruiser/Destroyer". This was a design project from the early 1950s, and aimed to replace the roles of the cruiser and destroyer by a single all-purpose design. However, this proved to be unworkable, for a variety of reasons, and was cancelled towards the end of 1954. The first design for what would become the 'County' class displaced about 4800 tons, and was armed with 3 twin 4.5 in gun turrets, and was produced in January 1955. Later in the year, the 'County' class design was merged with a design for a guided missile destroyer, using the Sea Slug missile. The project was given additional impetus by the cancellation of a guided missile cruiser design.

By 1957, the design had become mature enough to be presented to the Board of Admiralty. It displaced 6000 tons, and had a length of 505 ft. It was expected to achieve 30.5 knots. The design was armed with two twin 4.5in mountings, eight anti-submarine torpedoes and an anti-submarine mortar. It also had a twin Sea Slug launcher, with 18 missiles. Of these missiles, it was thought necessary that fourteen have conventional warheads, and the remaining four have nuclear warheads. However, to store these nuclear warheads, major changes were needed in the design. To make these changes, the torpedo tubes had to be removed. As this significantly weakened the ship's ASW capabilities, helicopter capabilities were investigated. These would need the anti-submarine mortar to be removed, but it was thought that the helicopter would entirely compensate for this loss, and those of the torpedoes. The first design with a helicopter had a landing space for an S.55 helicopter, but no hangar space, or ability for maintenance and refueling. However, as the design evolved, it received the ability to operate a Westland Wessex, with a hangar and support facilities. Eight ships were laid down to the 'County' Class design between 1959 and 1966, and they gave long service with the RN. Two ships served in the Falklands War, and four were sold to Chile, with whose navy they served until 2006.

As the first County Class were being laid down, the RN began design work on the Leander class frigates. These were essentially updates to the Type 12 frigates, which had been designed at the start of the 1950s. The advancing pace of technology, and the growing need for fleet escorts, had made the Type 12s somewhat obsolete - they were designed for convoy escort work, and didn't have the cruising speed necessary for fleet work. The Leanders replaced obsolete Bofors guns with Sea Cat missile launchers for point air defence. They lost an anti-submarine mortar and eight torpedo tubes, compared to the Type 12, but gained provision for a Westland Wasp helicopter.

Similarly, the three Tiger class cruisers were rebuilt over 1964-1968 to act as helicopter cruisers. While there had been a design project for a purpose built escort helicopter cruiser, this was postponed due to the entry into service of the 'County' class, and spending on Polaris submarines. Instead, the Tigers became the quickest way to get helicopters into the fleet. The redesigned Tigers were meant to form an anti-submarine helicopter force, giving the fleet a stand-off capability against submarines. The redesign involved the removal of a twin 6 in turret, and the addition of hangar space for four Wessex helicopters, with a flight deck capable of launching two simultaneously.

Helicopters greatly added to the ASW capabilities of British fleet escorts, giving them an over-the-horizon capability, as well as more sensors and greater flexibility. Helicopters allowed less tonnage to be dedicated to ASW weaponry below decks, allowing better use of space. Shifting helicopter capability off carriers to their escorts increased the capabilities of both ships - the carriers no longer had to dedicate time and space to launching and supporting ASW helicopters and could concentrate on their main roles of launching CAPs and strikes. I'm not aware of any opposition to it, amongst RN designers. They tended to recognise the increase in ability helicopters offered.

Sources:

Rebuilding the Royal Navy: Warship Design Since 1945, David K Brown, George Moore, Seaforth 2012

British Destroyers and Frigates: The Second World War and After, Norman Friedman, Seaforth 2012

Helicopters were simply an evolution of naval aviation; in some ways, from the very earliest naval aviation, [manned kites] (http://www.fleetairarmoa.org/fleet-air-arm-history-timeline), demonstrated by Samuel Cody in 1903. Some German U-boats in World War II carried [Focke Achgelis Fa 330 rotor-kites] (http://www.uboat.net/technical/bachstelze.htm) as a (not terribly successful) method of increasing spotting range, and the Royal Navy conducted some experiments with powered autogyros before the helicopter was perfected.

From the First World War, battleships and cruisers frequently carried seaplanes, launched by catapult and recovered with cranes; it was tried with a few destroyers such as [USS Pringle] (http://www.usspringle.org/PringlePic2.htm) and a couple of other Fletcher class ships, but wasn't successful. As with the various kites/gyros the original purpose was primarily reconnaissance and spotting. The offensive potential of seaplanes was also realised, Japanese Farman seaplanes from the Wakamiya mounting the first naval air raids in 1914.

Helicopters started to see operational service towards the end of the Second World War, with the US Navy and Royal Navy early adopters. One early role was operating with aircraft carriers to recover aircrew ; the light fleet carriers first deployed by the Royal Navy to Korea from 1950 still carried a [Supermarine Sea Otter] (http://www.iwm.org.uk/collections/item/object/205119941) seaplane; these were replaced with Westland Sikorsky Dragonflies (the RN version of the Sikorsky H-5) in 1952. As helicopters became more powerful and versatile they could fulfil more roles, with anti-submarine warfare (ASW) becoming a key role in the cold war (again, echoing earlier fixed-wing aviation such as the Fairey Swordfish operating from escort carriers to cover Atlantic convoys), helicopters being common on frigates and destroyers from the 1960s.

The first to land a rotorcraft on a ship was Juan de la Cierva in 1934 (a C.30 model autogyro on the Spanish seaplane tender Dédalo). However, the main driving force behind the development seems to be Reginald Arthur Charles Brie, who was an employee of Cierva's company at the time, and demonstrated its products' capabilities to land in (and later, take off from) very small spaces, notably a 90' by 30' platform on the Italian cruiser Fiume. In WW2, he first commanded an autogyro unit used to calibrate radars, then the Technical Development Unit of RAF's Central Landing Establishment. Later, he promoted the use of and helped experimenting with autogyros in the USA, and was the only British pilot to fly the prototype of R-4. He realized how useful actual helicopters' ability to hover is in naval operations, and was the first to land one on SS Daghestan early in 1944. On 23 May 1944, the six Aircraft Repair Units of Project Ivory Soap set sail, each with two R-4Bs on board.

The primary role of helicopters on light warships has been to deploy dipping sonar to detect submarines, and to launch torpedoes or other anti-submarine weapons to destroy submarines.

Helicopters if armed with suitable missiles can also attack surface ships, extend the scouting range of the mother ship, and engage in various re-supply, personnel transfer, or search and rescue operations.

It might be difficult to determine whose idea it was because it wasn't a post WWII decision at all. During WWII, the Germans had a gyrocopter kite deployed from U-boats, and the British had a dedicated autogyro demonstration ship sunk in 1942.

During WWII, aircraft were shoehorned onto every ship that could carry them. Most all cruisers had catapult launched seaplanes, the USN experimented with Fletcher class destroyers carrying seaplanes, and the British even went to the extreme of fitting catapult based land planes to freighters to provide some minimal air cover during the Battle of the Atlantic--the pilot would have to ditch after he ran out of gas and be picked up by a ship, or try and make it to a landing strip.

All this because being able to spot enemy ships before they can see you is critically important. The only thing keeping helicopters off of ships was that they were still in development, because they were obviously better for ship borne use than a seaplane. Seaplanes need a hanger, a heavy catapult to launch them, and a big crane to bring them back on board. A helicopter just needs the hanger, and a flat clear place to land. And a helicopter can potentially be recovered in rougher seas than a seaplane can since it doesn't need to land on the water first.